Let-a-b-c-be-three-unit-vectors-such-that-3a-4b-5c-0-Then-prove-that-a-b-c-are-coplanar-

Question Number 42521 by rahul 19 last updated on 27/Aug/18

Let \vec{a}, \vec{b}, \vec{c} be three unit vectors

such that 3 \vec{a} + 4 \vec{b} + 5 \vec{c} = 0 . Then prove

that \vec{a}, \vec{b}, \vec{c} are coplanar .

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Aug/18

w e h a v e t o p r o v e (\vec{a} \times \vec{b}) . \vec{c} = 0

3 \vec{a} + 5 \vec{c} = - 4 \vec{b}

(3 \vec{a} + 5 \vec{c}) \times \vec{b} = - 4 \vec{b} \times \vec{b}

3 \vec{a} \times \vec{b} + 5 \vec{c} \times \vec{b} = 0

3 \vec{a} \times \vec{b} = - 5 \vec{c} \times \vec{b}

3 (\vec{a} \times \vec{b}) . \vec{c} = - 5 (\vec{c} \times \vec{b}) . \vec{c}

h e n c e

3 (\vec{a} \times \vec{b}) . \vec{c} = 0 s o (\vec{a} \times \vec{b}) . \vec{c} = 0

h d n c e p r o v e d

Commented by rahul 19 last updated on 31/Aug/18

thanks sir.